Some cash flows involve the payments or receipts in gradients by same amount. In other words, the expenditure or the income increases or decreases by same amount. The cash flow involving such payments or receipts is known as uniform gradient series. For example, if the cost of repair and maintenance of a piece of equipment increases by same amount every year till end of its useful life, it represents a cash flow involving positive uniform gradient. Similarly if the profit obtained from an investment decreases by an equal amount every year for a certain number of years, it indicates a cash flow involving negative uniform gradient. The cash flow diagrams for positive gradient and negative gradient are shown in Fig. 1.3 and Fig. 1.4 respectively.

Fig 1.13 Cash flow diagram involving a positive uniform gradient

Fig 1.14 Cash flow diagram involving a negative uniform gradient

The present worth, future worth and the equivalent uniform annual worth of the uniform gradient can be derived using the compound interest factors. The generalized cash flow diagram involving a positive uniform gradient with base value ‘B' and the gradient ‘G' is shown in Fig. 1.15a. The cash flow shown in Fig. 1.15a can be split into two cash flows; one having the uniform series with amount ‘B' and the other having the gradient series with values in multiples of gradient amount ‘G' and is shown in Fig. 1.15b. This gradient series is also know as the arithmetic gradient series as the expense or the income increases by the uniform arithmetic amount ‘G' every year.